# Find the general solution to the following second

Find the general solution to the following second order differential equations.
$y{}^{″}-5y=0$
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Jambrichp2w2

First finding the solutions to the given second-order differential equation by forming the auxiliary equation
Let us take $\frac{dy}{dx}=D$
Then we have,
${D}^{2}-5=0$
${D}^{2}=5$
$D=±\sqrt{5}$
We know when the solutions to the auxiliary equation are identical and of opposite sign then the general solution to the given differential equation is
$y={c}_{1}{e}^{at}+{c}_{2}{e}^{bt}$
Here,

Therefore the general solution to the given differential equation is
$y={c}_{1}{e}^{\sqrt{5}t}+{c}_{2}{e}^{-\sqrt{5}t}$

Jeffrey Jordon